IZA DP No. 2776

Household Choices of Child Labor and Schooling:A Simple Model with Application to Brazil

Diana KrugerRodrigo R. SoaresMatias Berthelon

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Forschungsinstitutzur Zukunft der ArbeitInstitute for the Studyof Labor

May 2007

Household Choices of Child Labor and

Schooling: A Simple Model with Application to Brazil

Diana Kruger Pontificia Universidad Católica de Valparaíso

Rodrigo R. Soares

University of Maryland, Catholic University of Rio de Janeiro, NBER and IZA

Matias Berthelon

Pontificia Universidad Católica de Valparaíso

Discussion Paper No. 2776 May 2007

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IZA Discussion Paper No. 2776 May 2007

ABSTRACT

Household Choices of Child Labor and Schooling: A Simple Model with Application to Brazil*

This paper develops and estimates a simple structural model of household decisions regarding child labor and schooling. We argue that part of the conflicting results from the previous literature – related to the effect of improvements in economic conditions on child labor – derives from the different income and substitution effects implicit in different types of income variation. Our model leads to an empirical specification where income and substitution effects can be clearly identified. We apply our model to Brazil and use agricultural shocks to local economic activity (coffee and overall agricultural production) to distinguish between the effects of increases in household income and increases in the opportunity cost of children’s time. The results show that higher parental wages and household wealth are associated with lower child labor and higher school attendance. Nevertheless, conditional on family income and socioeconomic status, exogenous temporary increases in local economic activity are associated with increased opportunity cost of children’s time and, therefore, higher child labor and lower schooling. The results reconcile economic theory with seemingly contradictory evidence from the previous empirical literature. JEL Classification: D13, J22, 012 Keywords: child labor, schooling, generalized ordered logit, Brazil Corresponding author: Rodrigo R. Soares Department of Economics University of Maryland 3105 Tydings Hall College Park, MD 20742 USA E-mail: soares@econ.umd.edu * This paper benefited from the excellent research assistance of Daniela Zapata, and from comments from Marta Rubio Codina, Áureo de Paula, Claudia Sanhueza, Richard Williams, and seminar participants at the 2006 Northeast Universities Development Consortium Conference (NEUDC 2006, Cornell University), the XXVIII Meeting of the Brazilian Econometric Society (SBE 2006, Salvador), Fordham University, IPEA-Rio, Universidad de Chile, and UFRGS-PPG. Kruger and Berthelon received financial support from the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT), Chile, through FONDECYT Project No. 1050436 and International Cooperation Grant No.7050212. The usual disclaimer applies.

1

1 Introduction This paper develops and estimates a simple structural model of household decisions

regarding child labor and schooling. Though both the theoretical and empirical literatures on

child labor have blossomed in recent years, there remains a gap between the two. We argue that

part of the conflicting results obtained in the empirical literature – related to the effect of

improvements in economic conditions on child labor – derives from its lack of theoretical

structure. Our model leads to an empirical specification where the income and substitution

effects from different components of family income can be clearly identified. We show that the

effects of these components are different according to the margin of choice faced by the family,

and incorporate these restrictions in the estimation. As expected, our empirical results using

Brazilian data show that family wealth tends to reduce the incidence of child labor and increase

school attendance, while, conditional on family wealth, increases in economic activity (or in the

opportunity cost of children’s time) are associated with increased child labor and reduced school

attendance. Most of the conflicting results from the previous empirical literature can be easily

understood as a consequence of its incapacity to distinguish between the income and substitution

effects implicit in different types of income variation.

Child labor has been identified as an important determinant of the persistence of poverty

in developing countries. Inefficiently high levels of child labor – due to credit constraints or to

general equilibrium effects on wages – reduce human capital accumulation by children, therefore

reducing future wages and reproducing poverty and inequality. Baland and Robinson (2000)

show that, even when socially inefficient, child labor may exist due to the incapacity of parents

to borrow against the future income of children. Basu and Van (1998), in a multiple equilibria

model, stress an alternative mechanism in which child labor is both a cause and a consequence of

poverty: in a “good” equilibrium, when market wages are high, parents choose not to send their

children to work; whereas in a “bad” equilibrium, when wages are low and families are poor,

parents send their children into the labor force. Along similar lines, Dessy (2000) finds that there

is a critical level of adult wages below which child labor is supplied.1 Ranjan (2001) also shows

that credit constraints lead to inefficiently high levels of child labor, which, in turn, are related to

greater income inequality.

1 An exception in the theoretical literature is the model developed by Rogers and Swinnerton (2004), where low-income parents who anticipate future transfers from their children invest more in children’s present education, whereas high-income parents do not expect or need such transfers and, therefore, invest less in the human capital of children. Though theoretically consistent, this model does not seem particularly relevant to analyze the current situation in most developing countries.

2

In these models, the market solution leads to a situation where it would be socially

efficient to reduce children’s labor supply and increase schooling. In such settings, child labor

can be an intergenerational source of poverty traps: poor children work today, obtain less

schooling and become low productivity workers, earning low wages in the future (as suggested

by the evidence presented in Emerson and Souza, 2003).2

Empirical work on the determinants of child labor has spanned a wide range of different

settings and experiments. Edmonds (2005a and 2005b), for example, finds that improvements in

economic status explain most of the decline in child labor in Vietnam, while anticipated cash

transfers to the elderly in South Africa are associated with increased schooling and reduced labor

supply by children. Bourguignon et al (2003) and Cardoso and Souza (2004) find that, in Brazil,

conditional income transfers from the Bolsa Escola program increased the likelihood of

schooling, but had no significant impact on the incidence of child labor.3 Beegle et al (2006) find

that, in Tanzania, negative agricultural shocks (reports of value of crop losses due to insects,

rodents, and other calamities) increase the number of hours worked by children and reduce

school enrollment; they also show that households with a sufficiently high level of assets are able

to fully offset the shocks. These results suggest that poverty and liquidity constraints are

important determinants of household decisions regarding children’s allocation of time.

But other empirical evidence reaches conclusions that may seem puzzling at first sight.

Barros et al (1994) find that, in the eight largest metropolitan areas of Brazil, child labor is

higher during periods of low poverty and high economic growth, rather than during periods of

economic downturns and high poverty. Similarly, also looking at urban Brazil, Neri and Thomas

(2001) find that children are more likely to repeat a grade and more likely to work during periods

of economic growth, while Duryea and Arends-Kuenning (2003) find that incidence of child

labor is higher and educational outcomes are worse when average wages are higher. Kruger

(2006a and 2006b) finds that, in coffee producing regions of both Brazil and Nicaragua, children

are more likely to work and less likely to go to school during periods of improved economic

conditions due to coffee booms. Results such as these have led some authors – such as Barros et

al (1994) and Rogers and Swinnerton (2004) – to argue that there is at best a weak link between

income and child labor, and to question whether poverty and credit constraints are indeed the

sources of the problem.

2 Although most of the empirical literature has focused on the relationship between child labor and school attainment or enrollment, Gunnarsson et al. (2006) find that child labor leads to lower standardized test scores among grade school children of nine Latin American countries, thus harming the quality of schooling as well. 3 Bolsa Escola is a public cash transfer program conditional on children’s school attendance.

3

We claim that the seemingly conflicting results from the empirical literature are entirely

consistent with economic theory, once one realizes that different types of shocks to family

income – or different types of experiments – bring together different combinations of income and

substitution effects. Income changes that are mostly associated with changes in households’ full

income should represent either pure income effects or situations where income effects tend to be

relatively more important, and therefore should increase the demand for schooling and reduce

child labor. On the other hand, short term fluctuations in wages, income, or economic growth –

particularly when analyzed as deviations from a given secular trend – should be mostly

associated with increases in the opportunity cost of children’s time, given an expected present

value of full income. Therefore, these changes should isolate the substitution effect and bring

together increased child labor and reduced schooling.

In order to clarify how these different margins affect household choices regarding child

labor and schooling, we develop a very simple model that captures the main empirical

implications of the theoretical literature (Baland and Robinson, 2000, Basu and Van, 1998, and

Dessy, 2000). In addition to making explicit the argument developed in the previous paragraph,

the model leads to an empirical specification from a set of structural equations that can be

immediately taken to the data. The vast majority of empirical work analyzes the child labor and

schooling decisions as separate, discrete choices.4 However, in our model, child labor and

schooling are not mutually exclusive, and the response of households to changes in income may

vary with their level of consumption. The theory leads to a formulation where, in order to

account for all the relevant dimensions of the environment faced by families, child labor and

schooling decisions are characterized as a generalized ordered discrete choice problem. This

formulation highlights both the set of alternatives available to families (work only, schooling and

work, and schooling only) and the fact that families choosing each one of these different

alternatives may respond differently to marginal changes in exogenous variables. The theory also

highlights the necessity to distinguish between changes in family full income and children’s

wages for the different dimensions of the income and substitution effects to be adequately

identified.5

In order to implement the empirical specification, and given the limitations of the data

typically available, we exploit shocks to coffee and total agricultural production in Brazil as

4 Exceptions are Levison et al (2000) and Bourguignon et al (2003), who estimate multinomial logits. 5 In the micro-simulations performed by Bourguignon et al (2003), the conditional cash transfer program analyzed has potentially both income and substitution effects (by reducing the opportunity cost of schooling and, simultaneously, increasing family income). But the authors do not address this issue explicitly, nor try to separately identify these two components.

4

exogenous variation in the demand for unskilled labor. We concentrate the analysis on Brazil’s

coffee producing regions and rural areas, between 1993 and 2003, and use household data from

the Brazilian Household Survey (Pesquisa Nacional por Amostras de Domicílio – PNAD) and

agricultural production data from the Brazilian Census Bureau (Instituto Brasileiro de Geografia

e Estatística – IBGE). Controlling for family income and wealth, and for secular trends in

income, we are able to distinguish between the effects of family income and increased demand

for child labor (due to shocks to local economic activity). We find that, conditional on family

socioeconomic status and wealth, and on long-term growth, exogenous shocks to local economic

activity are associated with increased child labor and reduced schooling. Nevertheless, family

socioeconomic status and wealth – as measured by hourly wage and job tenure of the head of the

household, non-labor income, and ownership of various durable goods – are associated with

reduced child labor and increased schooling.

Additionally, in conducting various robustness checks, we identify the role of a series of

demographic correlates of child labor. Older children are more likely to work, while children

with higher educational attainment for a given age are more likely to be in school. Girls are more

likely to be in school and not working, while children living in rural areas are more likely to be

working and not in school. Conditional on household wealth and socioeconomic status, children

living in households with many children are more likely to work and less likely to be in school.

The remainder of the paper is organized as follows. In section 2, we develop a theoretical

model of child labor and schooling, and derive its empirical specification. In section 3, we

describe the data used in the analysis and discuss the empirical implementation of the model. In

section 4, we present and discuss the results. Finally, section 5 concludes the paper.

2 A Simple Model of Child Labor and Schooling 2.1 The Household Problem

This section develops a simple model of the joint household decision regarding child

labor and schooling. We concentrate on a simplified version of the household problem in order to

obtain a model that can be immediately taken to the data, and to highlight the dimensions that are

added by considering the joint decision. Though formally different, our model shares the same

basic properties of the theory proposed by Basu and Van (1998). From an empirical perspective,

our theory shows that, depending on the household’s choice of child labor and schooling, it may

respond differently to changes in the economic environment. This partly explains some of the

seemingly contradictory results obtained in the previous empirical literature.

5

Consider an economy where parents make all the relevant decisions. Since we want to

emphasize the different roles of family vis-à-vis child’s income in determining the labor supply

and schooling decision, we assume that each household has only one parent and one child. The

household derives utility from consumption and from the human capital of the child according to

the utility function

hc)h,c(U βσ

σ+= , (1)

where c is household consumption, h is the human capital of the child, and β and σ are constant

parameters, with 0 < σ < 1 and β > 0.

Consumption goods are purchased with income from adult and child labor. Assume that

parents participate fully in the labor market, so that their labor supply is fixed at the total amount

of labor time available (tp). Consumption satisfies the following budget constraint:

c ≤ wclc + wptp, (2)

where wc is the child wage, wp is the adult wage,6 and lc is the labor supply of the child.

The child’s time has to be allocated between work and investments in human capital

according to

lc + ec = tc, (3)

where ec is the time spent on investments in human capital by the child, and tc is the total amount

of time available for the child.

We abstract from the material costs of investments in education and assume that human

capital is produced only with the time of the child, according to the technology h = αecexp(v),

where α is a technological constant and v is an individual specific factor. Several family and

individual characteristics – ranging from education of parents to idiosyncratic ability or luck –

may affect the productivity of investments in human capital. These are summarized in the term v.

6 In principle, the adult wage depends on the level of human capital previously accumulated by the parent. We do not deal with this explicitly here, but it is the motivation behind the fact that the household attaches positive value to the human capital of the child (human capital is translated into higher future earnings).

6

We model v as being a linear function of a vector of demographic characteristics of the

household (x) and a random term (ε), such that v = γ′x + ε.

Writing down the full income constraint and substituting for h in the utility function, the

household problem can be stated as

.tosubject

)(expmax},{

ppcccc

cec

twtwewc

vecc

+≤+

+ βασ

σ

(4)

This very simple framework displays the same basic empirical implications stressed in

the original work of Basu and Van (1998). First, both children and adults can earn wages, so that

their labor supplies are seen as substitutes from the perspective of generating income for the

household (Substitution Axiom). Second, since preferences are quasi-linear in the human capital

of the child, household demand for child’s education respects what Basu and Van (1998) call the

Luxury Axiom. In other words, for sufficiently low family consumption, the marginal utility of

consumption is so high that the family allocates all of the child’s time to the labor market. As

family consumption grows and the marginal utility of consumption declines, the family

eventually starts investing some of the child’s time in acquiring education and, from this point

on, additional family resources are devoted entirely to investments in the child’s human capital.7

This remains true until the child dedicates her time fully to schooling, when again additional

resources start being devoted to household consumption. This is precisely the pattern that Basu

and Van (1998) try to generate with their model. The only difference is that the minimal level of

consumption, which in their case is given by what they call the subsistence level, here depends

also on the wage that the child faces on the market. In other words, when deciding what is

minimally acceptable to the family, parents are actually comparing the future benefits from the

child’s education with the current market value of the child’s labor. In addition, our model leads

to an empirical specification that can be immediately taken to the data.

Under these circumstances, the static nature of the model can be reinterpreted as

describing an environment where families face credit constraints in their decisions about

consumption and investments in children. In this specific context, credit constrains can take on

7 If the child’s time was not an input in the production of human capital, all additional resources would indefinitely be invested in the human capital of the child, and household consumption would never grow beyond what Basu and Van (1998) call the subsistence level. But since child’s time is needed to produce human capital, this model generates exactly the same pattern discussed by these authors.

7

two forms: the usual lack of access to capital markets, and, in addition, the inability of agents to

transfer debt to future generations, even with access to capital markets. In principle, with agents

having access to capital markets, the transfer of debt across generations could be a way of taking

advantage of higher returns to investments in human capital of children (as discussed at length in

Becker, 1981). But this possibility is typically not allowed in modern societies, therefore

introducing an intrinsic dimension of credit constraint in intergenerational problems. Since both

types of credit constraints are important issues for poor families in developing countries, and

these are the relevant families when discussing the phenomenon of child labor, we keep this

interpretation of the model throughout the paper.

The family decision regarding child labor and schooling becomes clear from the first

order conditions of the problem. Defining λ as the multiplier on the full-income constraint, first

order conditions for c and ec are, respectively,

cσ-1 = λ, and (5)

cwv λαβ<

>=)exp( (6)

with the inequality holding as < when ec = 0, as = when 0 < ec < tc, and as > when ec = tc. Given

the utility function, consumption will always be strictly positive as long as family income is

strictly positive.

The second first order condition characterizes the household decision regarding child

labor and schooling. If αβexp(v) < cσ-1wc, the marginal gain from investments in human capital is

lower than the marginal value of child labor, so the child works and does not go to school. If

αβexp(v) = cσ-1wc, the marginal value of one unit of time invested in human capital equals the

marginal value of one unit of time supplied in the labor market, so the child shares her time

between work and schooling. If αβexp(v) > cσ-1wc, the marginal value of one unit of time

invested in human capital is higher, so the child spends all her time studying.8

8 A fully recursive model, where parents utility depended on the child’s utility, which in turn would depend on wages, would lead to a similar characterization of the three alternative choices available to families. The only difference in this case would be that the term cσ-1 would be replaced by the inverse of the growth rate of consumption across generations, and another constant term (tp) would appear multiplying the left-hand side of the expression. Still, the basic trade-off would be between the future welfare of the child (in our model represented directly via a reduced form by h) and the current welfare of the family. We keep the formulation in the text because it is simpler and leads in a more direct way to our empirical specification. In the case of the fully recursive model, we would simply need to reinterpret the variable sp defined later on in the text.

8

Our goal is to characterize the discrete choice of the household between these three

states: child labor and no schooling, child labor and schooling, and no child labor and schooling.

As will be clear soon, the effect of changes in wealth and wages on family decisions is different

according to the situation in which the child is found.

2.2 Choices of Child Labor and Schooling

1st Case: Work and No Schooling

This choice is characterized by the inequality αβexp(v) < cσ-1wc. In this case, all the

child’s time is used as labor supply, such that lc = tc and ec = 0. Families in this situation already

send their children to work, and, for small changes in the economy, will never switch to a

situation where the children go to school and are entirely out of the labor market. What they

contemplate is the possibility of starting to invest part of the children’s time on schooling. From

the budget constraint, consumption is given by c = wctc + wptp, so that αβexp(v) < (wctc + wptp)σ-

1wc. Substituting the expression for v and using natural logarithms:

ε < ln(1/αβ) + lnwc +(σ – 1)ln(wctc + wptp) – γ′x. (7)

This formulation decomposes the income and substitution effects in the household

decision. The lnwc term represents the pure substitution effect, while family full-income (ln(wctc

+ wptp)) represents the pure income effect. For constant family income, a higher wage for the

child is associated with a higher opportunity cost of schooling and, therefore, a higher probability

that the child will work and not go to school. For constant wage of the child, higher family

income is associated with a lower probability that the child will work and not go to school. An

uncompensated change in wc, on the other hand, does not have an unequivocal effect. This

change brings together both income and substitution effects, and the final result depends on their

relative strength.

2nd Case: Schooling and No Work

This choice is characterized by the inequality αβexp(v) > cσ-1wc. In this case, all the

child’s time is used on investments in human capital, so that lc = 0 and ec = tc. For small changes

in the economy, families in this situation contemplate whether to start sending the children part-

time to the labor market. From the budget constraint, consumption is given by c = wptp, so that

the inequality can be written as αβexp(v) > wc(wptp)σ-1. Substituting the expression for v and

using natural logarithms:

9

ε ≥ (1/αβ) + lnwc +(σ – 1)ln(wptp) – γ′x. (8)

In this case, the child does not work, so the income effect is captured only by the full-

income of parents (ln(wptp)). Marginal changes in children’s wages do not affect the consumption

of the family and, therefore, have no income effect. But they do affect the opportunity cost of

investments in human capital. For these families, increases in the wage of children increase the

opportunity cost of schooling and unequivocally raise the probability that the children work and

go to school, instead of going to school only. On the other hand, for given children’s wages,

increases in parents’ income raise the probability that children go to school only, instead of

working and going to school.

3rd Case: Work and Schooling

This is the intermediary case, with αβexp(v) = cσ-1wc. In this situation, we have lc > 0 and

ec > 0. In words, the children share their time between work and schooling. From the first order

conditions, consumption is given by c = [αβexp(v)/wc]1/(σ – 1). Using the expression for v, this

situation is characterized by the following inequalities

ln(1/αβ) + lnwc +(σ – 1)ln(wctc + wptp) – γ′x ≤ ε

≤ ln(1/αβ) + lnwc +(σ – 1)ln(wptp) – γ′x. (9)

2.3 Empirical Specification

The household faces a discrete choice with three possible options in relation to the child:

work and no schooling, work and schooling, and schooling and no work. Define the discrete

variable J indicating the household choice as 0, 1, and 2, accordingly. The household decision

can be summarized as follows:

−−++≥

−−++<

≤−+−++

−+−++<

=

.')ln()1(ln/1if,2

,')ln()1(ln/1

')ln()1(ln/1if,1

,')ln()1(ln/1if,0

xtww

xtww

xtwtww

xtwtww

J

ppc

ppc

ccppc

ccppc

γσαβε

γσαβ

εγσαβ

γσαβε

This is a generalized ordered discrete choice model. If the random term ε is low enough,

the household chooses state 0; if it has intermediary values, the household chooses state 1; and if

10

it has sufficiently high values, the household chooses state 2. The difference from standard

ordered models lies in the fact that the threshold point in this case is not constant. The threshold

here is given by the explanatory variables, implicit in the difference between ln(wptp + wctc) and

ln(wptp), which varies across households.

Now index observations related to the ith child by the subscript i, with i ∈ I = {1, …, n},

where n is the number of observations in the sample. Assume that ε is randomly distributed with

distribution function F(.). Additionally, define Zij= 1 if child i is in state j, with Zij = 0 otherwise,

where j ∈ J = {0, 1, 2}. The likelihood function for the discrete choice problem discussed above

is given by

( )[ ]( )

( )( )[ ]

∏=

−−++−

×

−+−++−

−−−++

×−+−++

=n

i

Zippici

Z

iccippici

ippici

Ziccippici

i

i

i

xtwwF

xtwtwwF

xtwwF

xtwtwwF

L1

.')ln()1(ln/11

')ln()1(ln/1

')ln()1(ln/1

')ln()1(ln/1

2

1

0

γσαβ

γσαβ

γσαβ

γσαβ

(10)

There are two main problems with this formulation. First, for a significant fraction of

children, we do not observe market wages, and market wages may be endogenous to child labor

decisions in previous periods. And second, we do not observe full family income, which

becomes an even more difficult problem because of the previous issue.

In relation to child wages, we opt to use two alternative proxies for the level of demand

for child labor at the municipality where the child lives. This allows us to use all the children in

the sample, including the large number of those who do not work. The specific proxies that will

be used are based on the value of local agricultural production (coffee and overall agricultural

production), and will be discussed in detail later on. The basic idea is that these variables are

correlated with the local demand for unskilled labor, and at the same time have some degree of

exogenous variation due to the inherent uncertainty associated with climatic conditions and

agricultural production.

In relation to the second problem, we adopt the following strategy. The logarithm of

household full-income can be rewritten as ln(wcitc + wpitp) = lnwpi + lntp – lnspi, where spi =

tpwpi/(tpwpi + tcwci). The term spi gives the share of the family’s full-income that comes from

parents, or, alternatively, the relative importance of the child in terms of the income generating

power of the household. Notice that it refers to full-income, so that, given the educational level

of parents and the market wages faced by parents and children, it does not depend on household

11

decisions at that specific point in time. It will typically depend on family characteristics such as

educational attainment and age of the different members, gender of the child, composition of the

household, wealth, etc. Since 0 ≤ spi ≤ 1, we have lnspi ≤ 0, and the discrete choice problem

discussed before can be represented by

−−++≥

−−++<≤−−−−++

−−−−++<

=

,'ln)1(lnif,2

,'ln)1(lnln)1('ln)1(lnif,1

,ln)1('ln)1(lnif,0

*

**

*

ipiici

ipiciipiipici

piipicii

xww

xwwsxww

sxww

J

γσαε

γσαεσγσα

σγσαε

(11)

where α* = ln(tpσ-1/αβ). Given some distribution function F(.), the likelihood function for this

problem is analogous to the one in (10).

As mentioned before, the term spi will typically depend on household characteristics

capturing the wealth and income generating power of parents, as well as the potential market

wage of children. Assume that we can write spi as a function of a set of demographic

characteristics zi, as in lnspi = θ′zi. In principle, zi and xi can contain different elements or can be

the same vector. If they contain only different elements, the variables in zi will be responsible for

determining the shift in the threshold as family characteristics change. Alternatively, if zi and xi

are the same vectors, the threshold will be identified by allowing the coefficients on the variables

in xi to vary across the limits of the different categories. In the remainder of the paper, we

assume that lnspi = θ′zi. We save the discussion on the components of the vectors xi and zi for the

next section.

Other empirical issues arise because of the simplifying assumptions of the theoretical

model (e.g., households with only one child, parents employed full-time, etc.). These will be

dealt with in the empirical section, through the choice of sample and robustness checks

performed after the initial estimation.

3 Data and Variables 3.1 Data Sources

The data we use come from three different sources. All household level variables are

constructed from nine rounds of the Brazilian household survey (PNAD), which contains

information on characteristics of all household members. The PNAD is conducted nationally

throughout Brazil during the month of September of each year. We restrict the analysis to the

12

period between 1993 and 2003, for which consistent sampling methodologies and questionnaires

were maintained.9

The second source of data is the municipality-level surveys of agricultural production

administered each year by the Brazilian Census Bureau (Instituto Brasileiro de Geografia e

Estatística – IBGE), which we use to construct variables measuring the value of coffee

production per capita, as well as the value of overall agricultural production per capita. This

survey provides annual data of area planted, area harvested, quantity produced, and values of

most agricultural goods in Brazil. We also use municipality level GDP and population data from

the Brazilian Institute of Applied Economic Research (Instituto de Pesquisa Econômica Aplicada

– IPEA) and from IBGE.

3.2 Variables and Sample Selection

Our dependent variable follows the empirical specification laid out by equation (11) and

reflects the child’s school-work decision ordered according to what may be regarded as

increasingly “better” outcomes in terms of allocation of time.10 It is equal to 0 if the child works

exclusively, 1 if the child works and goes to school, and 2 if she only goes to school. The

variable is constructed based on two questions asking whether the child worked last week or at

any point during the past 12 months, and whether she is currently enrolled in school.11 Our

definition of child work is not restrictive and includes children who worked at any point during

the previous 12 months.

Three sets of independent variables constitute our main interest. First, we need variables

that would capture wage variations for both parents (wpi) and children (wci). Second, we need a

set of variables capturing the return to schooling for each particular child (xi). And, finally, we

need a set of variables indicating the relative importance of the child’s income in terms of the

full potential income of the household (zi), or, in a more general setting, in terms of the

household’s wealth.

9 We include the following years: 1993, 1995-1999, 2001-2003. In 1994 and 2000 PNAD was not conducted. 10 This statement is not entirely precise, since a family can always be made better off with the child working (in comparison with the child not working), as long as the child’s wage is sufficiently high. Nevertheless, these choices are indeed ordered from the perspective of the family choice (the statement would be precisely correct if we thought in terms of changes in the wage of the head of the household). 11 A fourth outcome would be if the child responded no to both questions, which could be interpreted as dedicating time exclusively to leisure. However, we believe that children are not likely to be completely idle, so that this response probably hides some type of work – domestic or in the market – or a transitory state. Rather than reassigning this outcome to one of the other groups, we do not include it in the empirical analysis; less than 5 and 4 percent of children in the rural and coffee samples, respectively, fall into this category.

13

Wages and Proxies for the Demand for Child Labor

For the first set of variables we use as parent’s hourly wage the head of the household

hourly wage, constructed from data on labor earnings and hours worked. In order to minimize

the problem of interaction between child labor and labor supply decisions of adults, and to bring

the sample closer to our theoretical model, we restrict the analysis to observations where the

head of the household is employed full-time. Later on we also introduce additional variables to

control for the interaction between labor supply of children and labor supply of other adults in

the household. We define working full-time for an adult as working al least 30 hours per week.

Then we define the head of the household as the spouse, in the main family unit of the

household, who has the highest hourly wage (in case both spouses work fulltime).12 We also

restrict the sample to children aged 10 to 14, to heads of the household between 18 and 65 years

of age, and to children who are relatives of the head of the household, in order to concentrate the

analysis on a more homogeneous group and to avoid including children who are treated

differently within the family unit.13

As mentioned in the previous section, we do not observe child wages for all children, so

we need to use proxies for the level of demand for child labor. In this respect, we use two

different strategies, each of them generating a different sample. In the first strategy (coffee

production sample) we use the value of coffee production per capita (in logarithms) as a proxy

for the level of economic activity, which may affect the opportunity cost of children’s time. In

the second one (agricultural production sample), we use the value of agricultural production per

capita (in logarithms). Both measures are constructed at the level of the municipality where the

child lives (see full description below).

We see these two measures as proxies for the demand for low-skilled labor, for which

child labor could potentially be a substitute. In municipalities where coffee or agriculture are

economically important, the value of coffee production or the value of agricultural production

are important indicators of local economic activity, and at the same time maintain a certain level

of exogeneity, given the uncertainties generally associated with climatic conditions and

agricultural production. Similar identification strategies were used by Schultz (1985), where

commodity prices served as instruments for the opportunity cost of women’s time, by Black et al

12 PNAD classifies the head of the household according to self-reporting. In the samples that we use, at least 84 percent of the self-reported heads of the household are also the spouses with the highest wage. In the rest of the paper all characteristics of the head of the household use our definition (based on the highest hourly wage among spouses working full-time). 13 Relatives are sons and daughters, and other relatives (including grandchildren and stepchildren).

14

(2003), where the price of coal was used as an instrument for men’s wages, and by Kruger

(2006a and 2006b), where coffee production was used as a proxy of the value of children’s time.

In the case of coffee production, we concentrate the analysis on municipalities where

coffee is an important economic activity. In this case, we see increased demand for child labor

not as being necessarily linked to harvesting or actual agricultural production. Where coffee is an

important activity, increased production may increase demand directly through demand for work

in agriculture, but also indirectly, through increased demand for labor in the transportation,

processing, and packaging of coffee, as well as in other auxiliary and satellite activities affected

by coffee cycles. So in order to concentrate the analysis on localities where coffee production is

indeed important, we restrict this sample to municipalities in the top 60% of coffee producing

municipalities. This selection criterion means that we include municipalities where the average

share of coffee production in total GDP between 1996 and 2002 – the years for which we have

both series – was at least 0.1 percent. In addition, to concentrate on localities where this shock

was indeed relevant for most of the population, we selected municipalities with total population

equal to less than 100,000 inhabitants.

For the agricultural production sample, we have a slightly different type of motivation in

mind. In this case, we are indeed thinking about increased demand for labor in agriculture

(harvesting, plowing, etc.), maybe due to unusually good climatic conditions or exceptionally

high commodity prices. In this case, we have an easier way to define the relevant sample. The

PNAD questionnaire already identifies households that are located in rural areas. So we restrict

the sample to rural households according to this variable, and use the value of total agricultural

production per capita as a proxy for the demand for child labor.

The incidence of the three possible outcomes for each year of our data is presented in

Table 1 separately for each of the two samples. Figures 1 and 2 also present the distribution of

weekly hours of work for children included in either of the two samples. As can be seen from the

table, the school-work decisions follow similar trends in both samples. Work only exhibits a

sharp declining trend with the incidence falling from more than 10% to less than 2% between

1993 and 2003 (in both samples). Work and school shows a clear declining trend in the

agricultural sample (23% in 1993 and 11% in 2003), but just a slightly declining trend in the

coffee production sample (37% in 1993 and 33% in 2003). Finally, the school only outcome

exhibits an increasing trend in both samples, although the increase is stronger in the coffee

production sample. From Figures 1 and 2, one can see that roughly 85 percent of working

15

children in our samples worked at least 10 hours per week at some point during the previous 12

months, and at least 75 percent worked more than 15 hours per week.

Table 2 presents the value of coffee and agricultural production per capita for

municipalities included in the samples using the restriction criteria described in the last page.

The value of coffee production per capita increases steadily between 1993 and 1999. In 2001, the

value of production collapses – along with the international and domestic prices of coffee – to 55

percent of the 1999 value and below the level observed at the beginning of the period.

Afterwards, production experiences a recovery, but still remains below the 1995 levels.

Agricultural production declines in the first half of the 1990’s and experiences a recovery in the

second half of the decade. As with coffee, agricultural production reaches the minimum value of

the sample in 2001, but then it experiences a sustained recovery that culminates in 2003, when

we observe the maximum value for the period analyzed. Our samples include typically 143

municipalities in the case of coffee production, and 545 municipalities in the case of agricultural

production.

Other Independent Variables and Additional Controls

In relation to the variables affecting the return to schooling (xi), we include years of

schooling, gender, race, and the age of the child, along with whether the household lives in a

rural area (for the coffee production sample). We also include the age of the head of the

household, years of education of the head of the household, and whether the head the household

is female. The age, gender and race of the child, previous investments in human capital, and rural

location may all affect the marginal gain from additional years of education. The age and

education of the household head, and whether the household is headed by a woman, may reflect

family characteristics that can be seen as direct inputs into the human capital production function

and, because of that, may affect the productivity of investments in education.

The importance of the child’s earning potential in relation to the household’s full income

(zi) depends, to a great extent, on a set of variables very similar to those determining the return to

schooling of the child. In this respect, we want variables capturing the child’s earning potential

and also indicators of the household’s full income (or wealth). The child’s age, educational

attainment, and the location of the household in a rural area may all affect her earning potential.

Parent’s tenure in the current job, other income of the household, and variables related to

household infrastructure are all closely related to the household’s full income and wealth. In

relation to household infrastructure, we consider variables that may indicate the socioeconomic

16

status of the family, such as the number of bedrooms per person, the availability of electricity

and the possession of a telephone line (fixed), a television set, a refrigerator, and a washing

machine. These are durable goods typically ordered in terms of family choices, so that they are

closer to indicating differences in socioeconomic status, rather than differences in tastes.

Variables included only in xi will appear with the same coefficient in the first and second

transition equations shown in expression (11). Variables included in both xi and zi will also

appear in both equations, but with different coefficients in each one. Finally, variables included

in zi, but not in xi, will appear only in the first equation, denoting the transition between state 0

(child labor and no schooling) and state 1 (child labor and schooling).

One important concern is related to factors not included in the discussion above, but that

may be correlated with the explanatory variables and with household decisions. To account for

the role of housework, intra-household substitution of labor, and dilution of family resources

across different children, we control for: the presence of other children in the household,

identified by particular age group (5 and below, between 6 and 9, and between 15 and 18); the

total number of siblings; the presence of a person above 60 years of age in the household;

whether both parents work; and whether the head of the household is a single parent. To account

for territorial variables that may be correlated to coffee and agricultural production, and to the

incidence of child labor, we use state fixed-effects in all regressions. Also, in order to allow for

further variations along this dimension, our robustness checks include as additional controls

medium-region fixed-effects (geographic units smaller than states that aggregate contiguous

municipalities), municipality characteristics such as GDP per capita and population, and state-

specific time dummies. Since these variables are not directly mapped into our simple theoretical

model, we let them enter in both xi and zi in the empirical specification.

We also test the robustness of the results to several different restrictions on the sample

and to alternative definitions of the dependent variable. Detailed discussion on these issues is

saved until the next section. Table 3 presents summary statistics for all explanatory variables

discussed here.

4 Results Drawing on the theoretical section, we assume that the error term ε follows a logistic

distribution, so that the choice problem described in equation (11) can be represented by a

17

generalized ordered logit model.14 Again, the dependent variable takes on the following three

values: 0 if the child did not attend school and worked at any time during the previous 12

months, 1 if the child worked and went to school simultaneously, and 2 if the child attended

school and did not work during the previous year. The generalized aspect of the model means

that the proportional odds assumption is not maintained, so that thresholds between the three

outcomes may vary according to the family’s characteristics.

Baseline Results

Table 4 presents the main results of our estimation. The first two columns contain the

estimated parameters for the two transition equations in the coffee sample, under our simplest

specification. This specification includes the value of coffee production per capita and the wage

of the head of the household (both constrained to be the same across the two equations), and

child and household characteristics, which are assumed to be part of xi and zi, so that they appear

in both transition equations, but with different coefficients in each one. Implicitly, we are

assuming that variables affecting the child’s return to schooling also affect the relative

importance of her income to the household, so that all variables included in xi are also considered

part of zi. In the third and forth columns, we present the results for the coffee sample including

the socioeconomic variables as additional controls.15 As these variables are related to the

importance of the child’s income to the household, but not necessarily to the child’s return to

schooling, they are assumed to be part of zi, but not of xi, and therefore appear only in the first

transition equation and are excluded from the second one. This is our baseline specification,

which will guide most of the discussion and subsequent robustness tests. The remaining columns

in the table present analogous results for the agricultural production sample, where the value of

coffee production per capita is replaced by the value of agricultural production per capita.

The coefficients presented in Table 4 refer to the effects of the explanatory variables on

the likelihood of working only compared to going to school and working (columns 1, 3, 5 and 7),

and on the likelihood of going to school and working compared to going to school only (columns

2, 4, 6 and 8). The estimated coefficients measure the effect of the independent variables on the

likelihood of higher-valued outcomes. So a positive and significant coefficient on the first

transition equation means that increases in the independent variable are associated, for families

14 We assume that the error term follows a logistic rather than a normal distribution because the estimation of generalized ordered probit models is particularly cumbersome from the numerical perspective. Our estimation was implemented using the commands and guidelines discussed in Williams (2006). 15 These coefficients are omitted from the table for clarity of exposition but are available upon request.

18

within that margin of choice, with a higher likelihood that the child works and goes to school,

instead of only working. Similarly, a positive and significant coefficient in the second transition

equation means that increases in the independent variable are associated, for families within that

margin of choice, with a higher probability that the child only goes to school, instead of working

and going to school simultaneously.

Results are very similar across the different specifications presented in the table. Also,

qualitative results are very similar when comparing the coffee production and the agricultural

production samples. Conditional on the hourly wage of the head of the household, higher values

of coffee or agricultural production per capita are associated with worse outcomes for children.

At the same time, conditional on the value of coffee or agricultural production, higher hourly

wages for the head of the household are associated with better outcomes for children. This

reveals that, conditioning on the hourly wage of the head of the household, on determinants of

the return to schooling and on the relative importance of the child’s income for the family, as

well as period-specific dummies, the value of coffee or agricultural production per capita

highlights the substitution effect from increased economic activity.16 Conditional on all these

factors, exogenous increases in economic activity are associated with increased opportunity cost

of children’s time and, therefore, increased child labor and reduced school attendance.

Most of the control variables also have the expected effects. Children who are older or

live in rural areas (for the coffee production sample) are more likely to be working and less

likely to be in school, while, conditional on age, children with more years of schooling are more

likely to stay in school. Also, children with more educated parents are more likely to be in school

and not to work, while children in families with better socioeconomic characteristics (not shown

in the table) are more likely to stay in school.17

In order to analyze the effect of the exogenous variable on the probability of occurrence

of the three alternative outcomes, we calculate the marginal effects for both the coffee and

agricultural production samples, using the most complete specification presented in Table 4

(columns 3-4 and 7-8). Results are found in Table 5.

Since coffee production, agricultural production, and the adult wage variables are

measured in natural logarithms, we can interpret the marginal effects as the impact of a 100

16 In reality, increases in demand for child labor also always bring together a bit of income and substitution effects. But the results show that our strategy, and the controls that we include in the estimation, tend to isolate the substitution effect. This result is consistent with that in Kruger (2006b). 17 Among the socioeconomic characteristics included, number of bedrooms per capita, tenure of the head of the household on the current job, and the presence of a telephone and a fridge in the household are the variables more closely related to the probability that the child attends school.

19

percent increase in the independent variables on the probability that each outcome occurs. For

example, in the coffee production sample, a 100 percent increase in the value of coffee

production leads to an increase of 0.04 percentage points in the proportion of children working

only (column 1), to an increase of 0.52 percentage points in the proportion of children working

and going to school (column 2), and to a reduction of 0.56 percentage points in the proportion of

children only going to school (column 3). In the agricultural production sample, a 100 percent

increase in the value of coffee production leads to an increase of 0.20 percentage points in the

proportion of children working only (column 4), to an increase of 1.30 percentage points in the

proportion of children working and going to school (column 5), and to a reduction of 1.50

percentage points in the proportion of children only going to school (column 6).

To get a sense of the magnitude of these changes, we divide the marginal effect by the

observed probability of each outcome, which is reported at the bottom of Table 5. For the coffee

production sample, the observed changes correspond to increases of 1 percent in the probability

of work only and 3.1 percent in the probability of work and schooling, and to a reduction of 0.70

percent in the probability of schooling only. For the agricultural production sample, they

correspond to increases of 2.9 and 3.9 percent in the probabilities of, respectively, work only and

work and schooling, and to a reduction of 2.6 percent in the probability of schooling only.

In relation to the wage of the head of the household, in the coffee production sample, a

100 percent increase is associate with a reduction of 0.26 percentage points in the fraction of

children only working, a reduction of 3.4 percentage points in the fraction of children working

and going to school, and an increase of 3.7 percentage points in the fraction of children only

going to school. In terms of the relative sizes of the different groups, these magnitudes represent

the following proportional changes: a reduction of 6.2 percent in the probability of work only, a

reduction of 20.2 percent in the probability of work and schooling, and an increase of 4.7 percent

in the probability of schooling only. In the agricultural production sample, an increase of 100

percent in the wage of the head of the household is associated with a reduction of 0.64

percentage points in the fraction of children only working, a reduction of 4.3 percentage points in

the fraction of children working and going to school, and an increase of 4.9 percentage points in

the fraction of children only going to school. In terms of the relative sizes of the different groups,

these magnitudes represent the following proportional changes: a reduction of 9.4 percent in the

probability of work only, a reduction of 12.0 percent in the probability of work and schooling,

and an increase of 8.5 percent in the probability of schooling only.

20

Overall, the responses of households to changes in economic activity and overall wealth

follow the pattern predicted by our theory. The shocks to local economic activity, once we

control for household characteristics, socioeconomic status, time trends, and state-specific

factors, do seem to isolate mostly the substitution effect from the increased demand for child

labor in the short-run. On the other hand, conditional on all other control variable,

socioeconomic status and the wage of the head of the household seem to isolate the income

effect, leading to better outcomes in terms of the allocation of time of children. The conflicting

effects found in previous papers are obtained here as different dimensions of the response of

families to increases in income and in the level of economic activity. Here, these results are

entirely consistent with economic theory and with the rational behavior of households.

Robustness Checks

In order to test the robustness of the results to different alternative hypotheses and to

address some issues not explicitly dealt with in the model, Table 6 presents a series of additional

results. These results refer to estimations that include further controls to our baseline

specification or that restrict the sample in other alternative ways. The table presents only the

main coefficients of interest (value of coffee or agricultural production per capita and the wage

of the head of the household), but we also discuss other results in the text (not presented in the

table) below.18

The first column in the table includes as additional controls (in both xi and zi) variables

related to family structure, which are not modeled explicitly in our theory, but which may affect

allocation of time or allocation of resources within the household. These may be related to

demand for household work, substitution of domestic or market labor across different members

of the household or dilution of family resources across different children. In order to account for

these possibilities, we include as additional independent variables a dummy indicating whether

both parents work, a dummy indicating whether the household has only one parent present, three

dummy variables indicating the presence of siblings aged between 0 and 5, between 6 and 9, and

between 15 and 18, a dummy indicating the presence of and elderly person in the household, and

a variable indicating total number of children present in the household. The main results are

virtually unchanged by the inclusion of these variables. Among the family structure variables,

number of children in the household, the presence of a sibling aged between 15 and 18, and the

fact that both parents work are all associated with worse allocations of time for children, towards

18 Results not reported are available upon request.

21

more work and less schooling. The other variables do not have robust and significant effects

across the different specifications.

The second column in Table 6 restricts the sample to only sons and daughters of the head

of the household, to avoid the comparison of children who may be treated differently by the main

family unit in the household. The third column, in sequence, changes the definition of child labor

to at least 15 hours of work a week at some point during the previous year, to characterize a

stronger attachment to the labor market. In both cases, results remain very similar to those

obtained with the baseline specification.

The fourth, fifth, and sixth columns control for factors that may be associated to

municipality characteristics and also to the incidence of child labor. In the fourth column, we

introduce fixed-effects for what the Brazilian Census Bureau (IBGE) calls medium-regions

(“meso-regiões”), which are geographic areas much smaller than states.19 In our case, the

average number of municipalities per medium-region is 3.3 in the coffee production and 4.4 in

the agricultural production sample. Medium-regions are sets of contiguous municipalities that

share similar geographic and economic conditions. The fifth column includes as independent

variables the natural logarithm of GDP per capita and population, both measured at the

municipality level. These may capture changes in local development and urbanization levels that

may be correlated to changes in agricultural production, and therefore could bias the results. The

sixth column then includes state or geographic region-specific time dummies, in order to account

for the possibility of differential trends in coffee or agricultural production across the different

areas of the country (see the previous footnote on the reasons why we use state-specific time

dummies in one case and geographic region-specific time dummies in the other). The results

remain significant and of the same order of magnitude in all cases. Particularly, in the case of the

coffee production sample, quantitative results are almost identical in the first two cases, and then 19 The high degree of non-linearity in the generalized ordered logit model stops us from introducing a large number of fixed-effects in the model. When we include municipality fixed-effects, for example, the maximum likelihood procedure fails to converge in several specifications, while the estimated coefficients become highly unstable in the few specifications that do converge (according to changes in the sample and control variables). This is why we choose to report the results using medium-region fixed-effects, which control for local heterogeneity without introducing the problem of estimating a large number of parameters in a highly non-linear setting. In addition, these fixed-effects control for local heterogeneity still leaving some degree of variation in the independent variables measured at the municipality level (this minimizes the problems discussed by Deaton, 1997, p.107-8, related to the increase in standard errors and in the imprecision of estimates when the variation in the independent variable of interest is relatively modest across-time within municipality). The non-linearity is a recurrent problem in the estimation of generalized ordered logit models, and tends to be even worse in the probit case (see Williams, 2006). We face a similar problem when estimating state-specific time dummies, when these fail entirely to converge in the case of the coffee production sample. In this case, we replace state-specific by geographic region-specific time dummies (according to the IBGE’s geographic classification of Brazil: North, Northeast, Centre-west, Southeast, and South). Also, a simple multinomial logit model does converge in this case, leading to results that are qualitatively similar to those reported in the table.

22

increase somewhat when we control for geographic region time dummies. In the case of the

agricultural production sample, quantitative results are reduced a little when we include medium-

region fixed effects or municipality characteristics, but the reduction is modest and significance

is still maintained.

For the coffee production sample, we also check the robustness of the results to the

definition of areas affected by coffee production. In the seventh column, we restrict the sample to

municipalities in the top 40% of coffee producing municipalities. Again, results remain

significant and quantitatively similar, though there is a small reduction in the coefficient on the

value of coffee production per capita and a more substantial reduction in the coefficient on the

wage of the head of the household.

Finally, the last two columns in Table 6 present results when the generalized ordered

logit model is estimated without the imposition of any constraint on its coefficients. For the case

of the coffee production sample, results seem to be quite similar to those obtained under the

estimation with constraints. For the agricultural production sample, the coefficients on the value

of agricultural production per capita are also quite similar to those obtained with the constraints,

but the ones on the wage of the head of the household are quantitatively quite different and,

surprisingly, not significant in the first transition equation. In more rigorous terms, in both

samples we cannot reject, at the 5 percent significance level, the hypothesis of equality across

transition equations of the coefficients on the value of coffee production and on the wage of the

head of the household.20 Overall, we cannot reject the constraints imposed by our very simple

theoretical model.

Additional Results

As a final exercise, we estimate our baseline specification for boys and girls separately,

and also for children in a different age group (15 to 18 years of age). These results are presented

in Table 7. As one might expect, boys’ responses to shocks to local economic activity are more

elastic than girls’ (columns 1 and 2). This is true for both samples (coffee and agricultural

production) and for both age groups. In relation to the response of the different genders to

changes in the wage of the head of the household, there is no clear pattern. Girls seem to be more 20 For the coffee production sample, the p-value for the joint Wald test for equality of coefficients across the different transition equations is 0.07; for the equality between the coefficients on the wage of the head of the household only, the p-value is 0.38, while for the equality between the coefficients on the value of coffee production only, it is 0.06. For the agricultural production sample, the p-value for the joint Wald test for equality of coefficients across the different transition equations is also 0.07; for the equality between the coefficients on the wage of the head of the household only, the p-value is 0.03, while for the equality between the coefficients on the value of agricultural production only, it is 0.42.

23

sensitive to the wage of the head of the household, but results are reversed in one of the

specifications and differences are relatively modest in others. Overall, older kids seem to be

slightly less responsive to shocks to local economic activity, maybe because they are already

engaged on market work on a more systematic basis (column 3). But opposite results are also

obtained in the case of boys between 15 and 18 years of age (column 4). In any case, both

quantitative and qualitative results are roughly similar across age groups and genders, and are

also quite close to the results obtained in our baseline specification.

5 Concluding Remarks In this paper, we develop a simple theoretical model of household choices regarding child

labor and schooling. The theory characterizes the household problem in a way that can be

represented by a generalized ordered discrete choice model, in which families can choose

between three alternative allocations of children’s time: work only, work together with

schooling, and schooling only.

We apply the model to Brazil, using agricultural shocks to local economic activity (from

coffee production and overall agricultural production) as a way to distinguish between the roles

of increases in family wealth (income effect) and in the opportunity cost of children’s time

(substitution effect) in determining the incidence of child labor. We find that household

characteristics associated with higher permanent income and wealth (or to less dependence on

child’s income) – hourly wage and job tenure of the head of the household, other sources of

income, and household infrastructure – are associated with lower incidence of child labor and

higher school attendance. At the same time, conditional on household wealth and socioeconomic

characteristics, and on long-term trends, increases in labor demand due to shocks to local

economic activity increase the opportunity cost of children’s time, therefore increasing the

incidence of child labor and reducing school attendance.

Our approach trusts more heavily on theory than the previous empirical literature on child

labor. As a consequence, we are able to understand the reasons behind some of its seemingly

conflicting results. We argue that our evidence related to family wealth and socioeconomic

status, and to increases in the short-term demand for labor, isolate, respectively, the income and

substitution effects present in different types of shocks faced by families. Generally, we show

that, in order to understand the effect of a certain change in income or in the level of economic

activity, one must understand how it affects the full income of the household and the opportunity

cost of children’s time. Only by understanding how a given shock affects these two dimensions

24

of the family problem one is able to understand its implications in terms of child labor and

schooling.

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Gunnarsson, Victoria, Peter F. Orazem and Mario A. Sánchez (2006). Child Labor and School Achievement in Latin America, The World Bank Economic Review, v20, n1, 31-54.

Kruger, Diana (2006a). Child Labor and Schooling During a Coffee Sector Boom: Nicaragua 1993-1998. In: L.F. Lopez-Calva (ed). Trabjo Infantil: Teoría y Evidencia desde Latinoamerica, Fondo de Cultura Económica de México, Mexico, forthcoming.

25

Kruger, Diana (2006b). Coffee Production Effects on Child Labor and Schooling in Rural Brazil, Journal of Development Economics, forthcoming.

Levison, Deborah, Karine S. Moe and Felicia Marie Knaul (2000). Youth Education and Work in Mexico. World Development, v29, n1, 167-88.

Neri, Marcelo C. and Mark Thomas (2001). “Household Responses to Labor-Market Shocks in Brazil, 1982-99.” Unpublished Manuscript, Fundação Getúlio Vargas.

Ranjan, Priya (2001). Credit constraints and the Phenomenon of Child Labor. Journal of Development Economics, v64, n1, 81-102.

Rogers, Carol Ann, and Kenneth A. Swinnerton (2004). Does Child Labor Decrease when Parental Income Rise? Journal of Political Economy, v112, n4, 939-46.

Schultz, T. Paul (1985). Changing World Prices, Women’s Wages, and the Fertility Transition: Sweden, 1860-1910. Journal of Political Economy, v93, n6, 1126-1154.

Williams, Robert (2006). Generalized Ordered Logit/Partial Proportional Odds Models for Ordered Dependent Variables. The Stata Journal, v6, n1, 58-82.

26

2.586

5.318 4.912

12.9

7.578

9.771

2.253

17.49

13.15

15.79

2.672

4.673

.4587 .4454

05

1015

20P

erce

nt

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71

Weekly hours worked

Source: Authors' estimates using PNAD data.

(Coffee sample)Fig. 1: Distribution of weekly hours worked

3.242

10.5812.16

31.37

10.7812.91

1.97

8.828

2.1883.775

.49131.474

.1345 .0983

010

2030

Per

cent

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71

Weekly hours worked

Source: Authors' estimates using PNAD data.

(Agriculture sample)Fig. 2: Distribution of weekly hours worked

27

Table 1: Distribution of Children by Year (%), Brazil, 1993-2003

Coffee Production Sample

Year

Work Only Work & School School Only N. Obs.

1993 11.50 22.87 65.63 3,157 1995 6.95 21.66 71.39 3,223

1996 4.50 17.01 78.49 2,892

1997 3.79 17.85 78.36 3,036

1998 3.56 17.27 79.17 2,919

1999 2.74 18.34 78.92 2,993

2001 1.77 10.91 87.32 2,714

2002 1.30 12.73 85.97 2,773

2003 0.71 11.34 87.95 2,664

Total 4.25 16.9 78.84 26,371

Agricultural Production Sample

Year

Work Only Work & School School Only N Obs

1993 14.81 37.01 48.18 6,077

1995 12.22 38.21 49.56 6,202

1996 9.7 30.6 59.7 5,585

1997 6.18 34.45 59.38 6,105

1998 4.64 35.52 59.84 5,929

1999 3.73 37.7 58.57 6,252

2001 2.56 36.08 61.36 4,690

2002 2.21 35.32 62.48 4,669

2003 1.84 32.76 65.4 4,359

Total 6.79 35.42 57.79 49,868 Notes: Sample restricted to children aged btwn 10 and 14 related to head of the household (heads of household restricted to full employed and aged btwn 18 and 65). Coffee production sample restricted to municipalities with less than 100,000 inhabitants in top 60% of coffee producing municipalities, and agricultural production sample restricted to rural households. Data from PNAD and IBGE agricultural surveys.

28

Table 2: Yearly Coffee and Agricultural Production per capita, Brazilian Municipalities included in the Sample, 1993-2003

Coffee Agricultural Year Production per

capita Number of Municip.

Production per capita

Number of Municip.

1993 107.29 142 516.46 539 1995 150.64 143 483.73 545

1996 157.05 142 453.11 543

1997 194.14 142 451.67 542

1998 206.56 141 474.04 543

1999 213.14 140 487.39 544

2001 94.55 140 422.37 418

2002 125.54 139 509.39 414

2003 123.09 139 641.84 415 Notes: Production per capita in 2000 R$ (reais). Sample restricted to children aged btwn 10 and 14 related to head of the household (heads of household restricted to full employed and aged btwn 18 and 65). Coffee production sample restricted to municipalities with less than 100,000 inhabitants in top 60% of coffee producing municipalities, and agricultural production sample restricted to rural households. Data from PNAD and IBGE agricultural surveys.

29

Table 3: Summary Statistics, Brazil, 1993-2003 Variable Coffe Production Sample Agricultural Production Sample

Obs MeanStd. Dev. Min Max Obs Mean

Std. Dev. Min Max

Income variables Value of Coffe Production p.c. 26,371 95.8 200.5 0 2343 Value of Agricultural GDP p.c. 49,868 688.3 1263.6 0 24568Hourly wage of head of household 26,371 1.6 2.8 0 172 49,868 0.9 1.7 0 94

Child Characteristics Years of Education 26,371 4.4 1.9 0 17 49,868 3.4 2.0 0 17 Female 26,371 0.49 0.50 0 1 49,868 0.47 0.50 0 1 Mixed 26,371 0.43 0.50 0 1 49,868 0.56 0.50 0 1 Black 26,371 0.05 0.21 0 1 49,868 0.04 0.20 0 1 Age 26,371 12.0 1.4 10 14 49,868 12.0 1.4 10 14 Lives in rural area 26,371 0.29 0.46 0 1 49,868 1.00 0.00 1 1

Family Characteristics Age of head of household 26,371 41.7 8.0 18 65 49,868 43.2 8.4 18 65 Education of head of hous. (years) 26,371 5.5 4.2 0 17 49,868 3.2 3.0 0 17 Female head of household 26,371 0.25 0.44 0 1 49,868 0.19 0.39 0 1

Wealth Characteristics Bedrooms per person 26,336 0.49 0.16 0.07 1.50 49,754 0.45 0.15 0.08 1.75 Has electricitiy 26,337 0.92 0.27 0 1 49,753 0.69 0.46 0 1 Has Telephone 26,326 0.26 0.44 0 1 49,747 0.05 0.21 0 1 Has television 26,313 0.83 0.38 0 1 49,732 0.59 0.49 0 1 Has refrigerator 26,336 0.75 0.43 0 1 49,745 0.46 0.50 0 1 Has washing machine 26,339 0.21 0.41 0 1 49,752 0.08 0.27 0 1 Tenure of head of household

(months) 26,371

109 109 0 696 49,868 163 144 0 696 Other income of household 26,371 36 149 1 7,025 49,868 25 91 1 7,025

Family Structure Both parents work 26,371 0.32 0.47 0 1 49,868 0.31 0.46 0 1 Head of the hous. is single parent 26,371 0.09 0.29 0 1 49,868 0.06 0.24 0 1 Sibs. 0-5 years living in household 26,371 0.30 0.46 0 1 49,868 0.37 0.48 0 1 Sibs.6-9 years living in household 26,371 0.42 0.49 0 1 49,868 0.51 0.50 0 1 Sibs 15-18 years living in household 26,371 0.39 0.49 0 1 49,868 0.45 0.50 0 1 Total number of siblings 26,371 1.43 1.28 0 9 49,868 1.91 1.58 0 12 Elderly member present 26,371 0.04 0.19 0 1 49,868 0.05 0.21 0 1

Notes: Monetary values in 2000 R$ (reais). Sample restricted to children aged btwn 10 and 14 related to head of the household (heads of household restricted to full employed and aged btwn 18 and 65). Coffee production sample restricted to municipalities with less than 100,000 inhabitants in top 60% of coffee producing municipalities, and agricultural production sample restricted to rural households. Data from PNAD and IBGE agricultural surveys.

30

Table 4 : Household Choices of Child Labor and Schooling - Generalized Ordered Logits, Brazil, 1993-2003

Coffee Production Agricultural Production (1) (2) (3) (4) (5) (6) (7) (8)

Coefficient Work/ Work & School

Work & School/ School

Work/ Work & School

Work & School/ School

Work/ Work & School

Work & School/ School

Work/ Work & School

Work & School/ School

Coffee Value (Ln) -0.045*** -0.045*** -0.044*** -0.044*** - - - - (0.014) (0.014) (0.014) (0.014) Agric. Value (Ln) - - - - -0.0625*** -0.0625*** -0.0624*** -0.0624*** (0.0211) (0.0211) (0.0212) (0.0212) Wage-head hhold. (Ln) 0.298*** 0.298*** 0.292*** 0.292*** 0.2091*** 0.2091*** 0.2039*** 0.2039*** (0.034) (0.034) (0.033) (0.033) (0.0245) (0.0245) (0.0247) (0.0247) Education (yrs) 0.210*** -0.0135 0.167*** -0.0122 0.2572*** 0.0992*** 0.2208*** 0.1007*** (0.026) (0.014) (0.028) (0.014) (0.0184) (0.0120) (0.0200) (0.0120) Child is female 0.625*** 1.037*** 0.670*** 1.036*** 0.5673*** 1.1062*** 0.6035*** 1.1046*** (0.079) (0.044) (0.078) (0.044) (0.0473) (0.0323) (0.0474) (0.0323) Mixed race 0.103 -0.00269 0.154* 0.000179 0.0334 0.0751** 0.0772 0.0739** (0.085) (0.053) (0.084) (0.053) (0.0526) (0.0356) (0.0525) (0.0355) Black 0.0164 0.0954 0.0523 0.0986 0.0306 0.2399*** 0.1311 0.2411*** (0.15) (0.11) (0.15) (0.11) (0.1031) (0.0824) (0.1034) (0.0826) Age -0.860*** -0.495*** -0.843*** -0.495*** -0.6375*** -0.4018*** -0.6293*** -0.4024*** (0.035) (0.017) (0.036) (0.018) (0.0205) (0.0105) (0.0205) (0.0105) Rural location -0.840*** -1.055*** -0.835*** -1.051*** - - - - (0.099) (0.089) (0.10) (0.089) Age-head hhold. -0.00636 -0.0000112 -0.0128** -0.00021 -0.0068** -0.0073*** -0.0138*** -0.0074*** (0.0050) (0.0027) (0.0051) (0.0027) (0.0028) (0.0016) (0.0031) (0.0016) Educ-head hhold. 0.146*** 0.0704*** 0.117*** 0.0715*** 0.1090*** 0.0680*** 0.0905*** 0.0685*** (0.016) (0.0075) (0.016) (0.0075) (0.0124) (0.0082) (0.0125) (0.0083) Female head hhold. -0.195** -0.0403 -0.142* -0.0455 -0.0457 0.0241 -0.0316 0.0233 (0.078) (0.053) (0.078) (0.053) (0.0588) (0.0388) (0.0608) (0.0389) Bedrooms/person 0.621*** 0.3520** (0.24) (0.1643) Electricity -0.108 -0.0269 (0.11) (0.0642) Telephone 1.178*** 0.5939** (0.28) (0.2737) Television 0.0993 0.1830*** (0.10) (0.0624) Refrigerator 0.188* 0.2500*** (0.099) (0.0669) Washing machine 0.309* 0.0517 (0.16) (0.1256) Tenure-head hhold. 0.0008*** 0.0008*** (0.0002) (0.0002) Other hhold income 0.00689 0.0331** (0.020) (0.0141) Constant 12.38*** 6.468*** 12.27*** 6.459*** 8.3273*** 4.4021*** (0.50) (0.27) (0.53) (0.28) (0.4199) (0.3553) N Obs 26.371 26.293 49.868 49.705 N Municipalities 143 143 623 623 Chi-Sq 15.377 15.911 12.207 12.284 Chi-Sq p-value 0,00 0,00 0,00 0,00 Notes: State and year fixed effects included in all specifications. Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Unit of observation is child. Dep var is categorical indicating whether child works only (0), works and goes to school (1), or goes to school only (2). Indep vars are value of municipality coffee or agricultural production per capita (ln), hourly wage of head of household (ln), education, female dummy, race dummies (mixed and black), age, rural dummy, age of head of household, education of head of household, female head of household dummy, number of bedrooms per capita, dummies indicating whether household has electricity, phone, tv, fridge, and washing machine, tenure of head of household in current job, other income of household (ln). Sample restricted to children aged btwn 10 and 14 related to head of the household (heads of household restricted to full employed and aged btwn 18 and 65). Coffee production sample restricted to municipalities with less than 100,000 inhabitants in top 60% of coffee producing municipalities, and agricultural production sample restricted to rural households. Robust standard errors clustered at municipality level. Data from PNAD and IBGE agricultural surveys.

31

Table 5: Household Choices of Child Labor and Schooling - Generalized Ordered Logits Marginal Effects, Brazil, 1993-2003

Coffee Production Agricultural Production (1) (2) (3) (4) (5) (6) Coefficient

Work Only Work- School

School Only

Work Only

Work & School

School Only

Coffee Value (Ln) 0,00039*** 0,00516*** -0,00555*** - - - (0,00013) (0,00166) (0,00179) Agric. Value (Ln) - - - 0,00196*** 0,01304*** -0,01500*** (0,00065) (0,00442) (0,00507) Wage-head hhold. (Ln) -0,00260*** -0,0341*** 0,03672*** -0,00640*** -0,04258*** 0,04898*** (0,00034) (0,00389) (0,00415) (0,00077) (0,00515) (0,00588) Education (yrs) -0,00148*** 0,00302* -0,00154 -0,00693*** -0,01726*** 0,02418*** (0,00029) (0,00174) (0,00181) (0,00067) (0,00273) (0,00286) Child is female -0,00602*** -0,12423*** 0,13025*** -0,01890*** -0,23931*** 0,25821*** (0,00087) (0,00629) (0,00656) (0,00151) (0,00694) (0,00733) Mixed race -0,00136* 0,00134 0,00002 -0,00243 -0,01534* 0,01778** (0,00073) (0,00646) (0,00663) (0,00166) (0,00834) (0,00854) Black -0,00046 -0,01155 0,01201 -0,00389 -0,05256*** 0,05645*** (0,00130) (0,01285) (0,01351) (0,00289) (0,01777) (0,01876) Age 0,00751*** 0,05468*** -0,06219*** 0,01974*** 0,07693*** -0,09667*** (0,00066) (0,00218) (0,00230) (0,00081) (0,00244) (0,00247) Rural location 0,00906*** 0,14480*** -0,15386*** - - - (0,00150) (0,01499) (0,01561) Age-head hhold. 0,00011*** -0,00009 -0,00003 0,00043*** 0,00135*** -0,00179*** (0,00005) (0,00032) (0,00034) (0,00010) (0,00038) (0,00039) Educ-head hhold. -0,00104*** -0,00795*** 0,00899*** -0,00284*** -0,01361*** 0,01645*** (0,00016) (0,00091) (0,00094) (0,00039) (0,00190) (0,00196) Female head hhold. 0,00131* 0,00445 -0,00576 0,00100 -0,00659 0,00559 (0,00076) (0,00658) (0,00677) (0,00194) (0,00890) (0,00932) Bedrooms/person -0,00553*** 0,00553*** -0,01104** 0,01104** (0,00216) (0,00216) (0,00517) (0,00517) Electricity 0,00092 -0,00092 0,00084 -0,00084 (0,00092) (0,00092) (0,00199) (0,00199) Telephone -0,00842*** 0,00842*** -0,01462*** 0,01462*** (0,00139) (0,00139) (0,00512) (0,00512) Television -0,00091 0,00091 -0,00584*** 0,00584*** (0,00101) (0,00101) (0,00203) (0,00203) Refrigerator -0,00176* 0,00176* -0,00779*** 0,00779*** (0,00096) (0,00096) (0,00207) (0,00207) Washing machine -0,00253*** 0,00253*** -0,00159 0,00159 (0,00122) (0,00122) (0,00378) (0,00378) Tenure-head hhold. -0,00001*** 0,00001*** -0,00002*** 0,00002*** (0,00000) (0,00000) (0,00001) (0,00001) Other hhold income -0,00006 0,00006 -0,00104** 0,00104**

(0,00018) (0,00018) (0,00045) (0,00045) Obs. Freq. 0,042 0,169 0,789 0,068 0,354 0,578 N Obs 26.293 49.705 N Municipalities 143 623 Chi-Sq 15911 12284 Chi-Sq p-value 0,00 0,00 Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Unit of observation is child. Effect of change in indep. variable on prob. of outcome (complete specification in Table 4). Indep vars are value of municip. coffee or agric. production per capita (ln), hourly wage of head of household (ln), education, female dummy, race dummies (mixed and black), age, rural dummy, age of head of household, education of head of household, female head of household dummy, bedrooms per capita, dummies indicating whether household has electricity, phone, tv, fridge, and washing machine, tenure of head of household in current job, other income of household (ln), and state and year fixed effects. Sample described in Table4. Data from PNAD and IBGE agricultural surveys.

32

Table 6: Robustness Checks for Household Choices of Child Labor and Schooling - Generalized Ordered Logits, Brazil, 1993-2003 No Constraints

Family

Structure

Sons and Daughters

≥ 15 Hours of Weekly

Work

Meso-

region F.E.

Municipality

Charact.

State/Region-Specific Time

Dummies

Top 40% Coffee

Production

Work /Work & School

Work & School/ School

Sample Coefficient

(1) (2) (3) (4) (5) (6) (7) (8) (9)

-0.0419*** -0.0447*** -0.0524*** -0.0451*** -0.0428** -0.0688*** -0.0380** -0.0726*** -0.0407*** Coffee Value (Ln) (0.014) (0.014) (0.013) (0.015) (0.0173) (0.015) (0.017) (0.015) (0.014)

0.284*** 0.2819*** 0.2501*** 0.276*** 0.299*** 0.3132*** 0.178*** 0.151** 0.206*** Wage-head hhold. (Ln) (0.034) (0.033) (0.035) (0.035) (0.0528) (0.0324) (0.036) (0.062) (0.036)

Coffee Production

N Obs 26.293 25.468 26.098 26.293 11.336 26.293 20.673 26.293 26.293

-0.0635*** -0.0628*** -0.0688*** -0.0482** -0.0424** -0.0624*** - -0.0648*** -0.0471** Agric. Prodn. Value (Ln)

(0.0207) (0.021) (0.021) (0.0237) (0.0215) (0.0216) (0.0215) (0.0189)

0.1878*** 0.2048*** 0.1664*** 0.1843*** 0.2468*** 0.2087*** - 0.0428 0.1154*** Wage-head hhold. (Ln) (0.0250) (0.024) (0.023) (0.0224) (0.0339) (0.0249) (0.0291) (0.0259)

Agricultural Production

N Obs 49.705 48.134 49.245 49.705 21.134 49.705 49.705 49.705

Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Unit of observation is child. Dep var is categorical indicating whether child works only (0), works and goes to school (1), or goes to school only (2). Indep vars include all controls from Table 4 (not shown). Family structure includes dummies for both parents working, single parent household, presence of siblings aged btwn 0 and 5, btwn 6 and 9, and btwn 15 and 18, number of siblings, and dummy for presence of elderly person. Sons and daughters restricts sample to sons and daughters of the head of household. More than15 hours of weekly work restricts sample to children that worked at least 15 hours. State/region-specific dummies includes state or region-specific time dummies (maximum likelihood in the cofee sample did not converge with state-specific dummies). Municip. charact. includes ln(gdp per capita) and pop. Last two columns, respectively, restrict sample to municip. in top 40% of coffee production and estimate complete model from Table 2 without constraints. Initial samples identical to that of Table 4. Robust standard errors clustered at municipality level. Data from PNAD and IBGE agricultural surveys.

33

Table 7: Additional Results for Household Choices of Child Labor and Schooling - Generalized Ordered Logits, Brazil, 1993-2003

(1) (2) (3) (4) (5) Sample Coefficient Boys Girls Ages 15-18 Boys 15-18 Girls 15-18

-0.0477*** -0.0371** -0.0355*** -0.0401*** -0.0299* Coffee Value (Ln) (0.015) (0.019) (0.013) (0.012) (0.017)

0.263*** 0.351*** 0.270*** 0.252*** 0.295*** Wage-head hhold. (Ln) (0.038) (0.053) (0.027) (0.033) (0.041)

Coffee Production

N Obs 13.534 12.759 17.205 9.588 7.617

-0.0690*** -0.0510** -0.0639*** -0.0758*** -0.0467*** Agric. Prodn. Value (Ln) (0.0227) (0.0218) (0.0155) (0.0176) (0.0167)

0.2178*** 0.1956*** 0.1267*** 0.1085*** 0.1558*** Wage-head hhold. (Ln) (0.0265) (0.0326) (0.0213) (0.0263) (0.0300)

Agricultural Production

N Obs 26.090 23.615 30.556 18.213 12.343

Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Unit of observation is child. Dep var is categorical indicating whether child works only (0), works and goes to school (1), or goes to school only (2). Indep vars include all controls from Table 4 (not shown). Basic coffee production sample restricted to municipalities with less than 100,000 inhabitants in top 60% of coffee producing municipalities, and agricultural production sample restricted to rural households. Robust standard errors clustered at municipality level. Data from PNAD and IBGE agricultural surveys. Sample restricted to children aged btwn 10 and 14 related to head of household (heads of household restricted to full employed and aged btwn 18 and 65). Additional results restrict sample to, respectively, boys, girls, children btwn 15 and 18, boys btwn 15 and 18, and girls btwn 15 and 18.